a = (x^3) - 4

PolynomialQuotient[a, x - (4^(1/3)), x]

PolynomialRemainder[a, x - (4^(1/3)), x]

(Subscript[q, 1]) = PolynomialQuotient[a, x - α, x]

(Subscript[q, 2]) = PolynomialQuotient[(Subscript[q, 1]), x - β, x]

Collect[(x - α) (x - β) (x - γ), 
      x]

\(q\_1 = PolynomialQuotient[a, x - Root[#\^3 - 4 &, 1], x]\)

\(PolynomialQuotient[q\_1, x - Root[#\^3 - 4 &, 2], x]\)

Solve[(Subscript[q, 1]) == 0, x]